Abstract: The fastening device has first and second fastening means fittable to the carpet and to the mat and which click together. The first fastening means are defined by a single part having two flanges integral with a hub and which are positioned on opposite sides of the carpet; and one of the flanges is shaped to permit passage through a hole in the carpet by rotating the single part. The second fastening means have a further two flanges integral with two corresponding hubs which fit together in a variable axial position through a hole in the mat to adapt the distance between the further two flanges to the thickness of the mat. The single part carries a male member which clicks inside an elastic female member carried by one of the flanges fitted to the mat.